In a similar fashion, the free energy contribution of a Fermi particle of energy \(\epsilon \)  [1]}
\(F(\epsilon ) = -\log \left(1+ e^{-\epsilon (p)}\right)\; , \quad \quad n(p) = \left.\frac{{\rm d}F(\epsilon )}{{\rm d}\epsilon } \right|_{\epsilon =\epsilon (p)} \; ,\) 
